We don't know anything about the circumstances of the kidnapping, except Graendal spoke of it as "all this trouble". She's most unlikely to have jumped in and taken away the enthroned ruler and his mate while the Ayyad watched.

She more likely captured them in their non doubt secluded private quarters, or even while they slept. Rulers don't carry around a ceremonial scepter all day long.

Graendal performed these kidnappings simply as a diversion, to make Sammael believe she had interests she didn't have in the East, likely just inspired by a tale about the cyclical rulers who died by "the will of the Pattern" told her by Jain Farstrider. She didn't investigate the nation as if she meant to use it, that's the whole point. In the same scene, Graendal has mounted a little diversion capturing rulers in Demandred's playground without knowing while Sammael has delusions about Demandred being in the south. The whole joke is that Graendal has learned just enough to present Shara to Sammael as an attractive ploy for a Forsaken. He didn't fall for it, he knew if she really had plans there she would never have given him clues. Graendal didn't pay attention to what happened there, thinking her kidnappings were the sole cause of chaos there, and Sammael didn't pay attention, thinking this was a Graendal diversion.

There's no good reason to conclude she would have learned of a scepter or paid any attention to stuff like that. The rulers were just puppets of the Ayyad and very young. The Sharans rarely ever saw them according to the BWB, as most dealings with them went through the Ayyad. Little about them would be known even by the Sharans.

Perhaps the scepter was an artefact linked to their prophecies and guarded by the Ayyad in the vein of Callandor - and they gave it to the Wyld - but it's also perfectly possible it was used by the Ayyad as a scepter for the one of their pair of puppets currently "ruling", and they gave it to Demandred as he replaced the male ruler.

The Ayyad may not have known it was a san'angreal. They're all female. According to the BWB their male children were kept prisoners in villages, sent after puberty to similar villages in other regions (to avoid inbreeding) and made to breed with the Ayyad. They are killed ritually at 21, sooner if they spark. Unless it's an error by Brandon, the only explanation why there were male Sharan channelers is that the Wyld forbade the factions of Ayyad who followed him from killing them, so he got himself the men between 16 and 21 whom he trained.

In any case it's possible the Sharans didn't know the scepter was a san'angreal before the LB. There are hints that Demandred's recognition by the Ayyad rested on using the TP.

It sounds very much like the Wyld was Rand all along. He "remade the world" to save the world, he slayed the Dragon, and he's the one who at the end have hidden powers without channeling. Demandred was a false Wyld, much in the vein of false Dragons.